The FE computed mode shapes of the aforementioned modes are shown in Fig. 19.
The goal of this work is to propose a numerical approach to compute modes in embedded helical structures, combining the so-called semi analytical finite element method and a radial perfectly matched layer technique.
Utilising a computationally efficient numerical slice modelling approach, the Virtual Crack Closure Technique (VCCT) is used to compute Mode-I and Mode-II ERRs induced by bi-axial bending.
The applicability of these methods to certain areas of structural dynamics is limited by two major factors: the lack of separate structural operators (mass, damping, and stiffness matrices), and the subsequent difficulty in computing mode shapes via eigenvalue decomposition.
Moreover, we confirm that the computed normal modes satisfy an energy conservation law for free-surface MHD with error smaller than 10−6.
The comparison with Abaqus finite element analyses is presented, demonstrating, for a wide variety of test cases, percent differences below 9% and a good accuracy of the computed buckling modes.
The displacement function of the strip element is expressed as the product of cubic Hermitian functions in the transverse direction and a set of computed static modes in the longitudinal direction.
Crack propagation angles are also determined along the deflected and inclined corner crack fronts based on the computed mixed-mode stress intensity factor distributions.
Because the code period estimates are less than half of the computed first mode period, peak displacements would be substantially underestimated using the code period estimates; any updating to recognize the eigenvalues would necessitate a series of iterative design refinements.
The angular resolution that can be achieved with the new processing scheme is predicted to be (155/Nm) degrees, where Nm is the highest order of computed response mode, for the higher orders.
